An iterative domain decomposition method is proposed for numerical analysis of three-dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the preconditioned conjugate gradient (PCG) procedure and the hierarchical domain decomposition method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann–Neumann (NN) preconditioner. Numerical results showed that the method was only effective for problems with a small number of subdomains. In this paper, we show its improvement with the balancing domain decomposition diagonal scaling (BDD-DIAG) preconditioner and show the asymptotic equivalence between BDD-DIAG and the simplified diagonal scaling (diag) preconditioner, which is derived from the following numerical evidences.

中文翻译：

---

静磁问题域分解法中预条件子的关系

提出了一种迭代域分解方法，用于以磁矢量势为未知函数的三维（3D）线性静磁问题的数值分析。迭代域分解方法与预条件共轭梯度（PCG）过程和并行计算中采用的层次域分解方法（HDDM）相结合。我们之前使用的预处理器是 Neumann-Neumann (NN) 预处理器。数值结果表明，该方法仅对少数子域的问题有效。在本文中，我们展示了平衡域分解对角缩放（BDD-DIAG）预处理器的改进，并展示了 BDD-DIAG 和简化对角缩放（diag）预处理器之间的渐近等价性，